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This is the chapter 4 for Business Dynamics and System Modeling Class
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Business Dynamics and System ModelingChapter 4: Behavior of the System
Pard TeekasapSouthern New Hampshire University
Outline
1. Fundamental modes– Exponential growth– Goal seeking– Oscillation
2. Interaction of the fundamental modes– S-shaped growth– S-shaped growth with overshoot– Overshoot and collapse
What are the system behaviors come from?
• The behavior arises from its structure• Structure consists of the feedback loops, stock
and flow, and nonlinearities created by the interaction of the physical and institutional structure of the system
Common modes of behavior in dynamic systems
Exponential Growth
Time
Goal Seeking
Time
Oscillation
Time
S-shaped Growth
Time
Overshoot and Collapse
Time
Growth with Overshoot
Time
Exponential Growth
• Arises from positive feedback• Pure exponential growth has the constant
doubling time• What is the examples of exponential growth?
Exponential Growth structure
RNet
IncreaseRate
State of theSystem
+
+
Time
State of theSystem
Example of exponential growth
0
2
4
6
1900 2000
0
2
4
6
0 400 800 1200 1600 2000
Bill
ion
Pe
op
le
Lower Bound
Upper Bound
Average Growth Rate:1900 - 1950: 0.86%/year (doubling time 80 years)1950 - 1997: 1.76%/year (doubling time 40 years)
0
300
600
900
1200
1920 1940 1960 1980 2000
Th
ou
sa
nd
Pe
op
le
Average Growth Rate:1926 - 1995: 3.5%/year (doubling time 20 years)1970 - 1995: 6.8%/year (doubling time 10 years)
0
3
6
1965 1970 1975 1980 1985 1990 1995 2000
80868080 80286386
486
Pentium
PentiumPro
Average Growth Rate:33%/year (doubling time: 2 years)
4004Best Fit Exponential
102
103
104
105
106
107
1965 1975 1985 1995
Mill
ion
Tra
ns
isto
rs/C
hip
0
4000
8000
1850 1900 1950 2000
Bill
ion
19
92
$/Y
ea
r Average Growth Rate 3.45%/yearDoubling Time 20 years
US Real GDP
World Population
US Prison Population
Transistors per Chip, Intel Microprocessors
Goal Seeking
Time
State of theSystem
Goal
CorrectiveAction
BDiscrepancy
+
-
+
Goal(Desired
State of System)
State of theSystem
+
Characteristics of goal seeking
• If the relationship between the size the gap and the corrective action is linear, the rate of adjustment is exactly proportional to the size of the gap and the resulting goal-seeking behavior is exponential decay
• Pure exponential decay is characterized by its half life
• What are the examples of goal seeking behavior?
Example of goal-seeking behavior
0
500
1000
1500
1987 1988 1989 1990 1991
Semiconductor Fabrication Defect Rate
Start of TQM Program
0
20
40
60
80
100
1978 1980 1982 1984 1986 1988 1990 1992
Nuclear Plant Load Factor
0
5
10
15
20
25
1950 1958 1967 1975 1983 1992
Television Share of All Advertising, US
0
5
10
15
20
25
1920 1940 1960 1980 2000
US Traffic Fatalities per Vehicle Mile
Oscillation
• The overshooting arises from the presence of significant time delays in the negative loop
• However, most real world oscillations is not perfectly regular. You shouldn’t expect it to be
• What are the examples of oscillation behavior?
Oscillation structure
BDiscrepancy
+
-+
State of theSystem
DelayCorrective
Action
Delay
Delay
+Administrative andDecision MakingDelays
Time
State of theSystem
Goal
Measurement,Reporting, andPerceptionDelays
Goal(Desired
State of System)ActionDelays
Example of oscillation behavior
-0.4
0.0
0.4
1850 1900 1950 2000
US Real GDP Deviation From Trend
70
75
80
85
90
95
1945 1955 1965 1975 1985 1995
Capacity Utilization, US Manufacturing
0
2
4
6
8
10
12
1945 1955 1965 1975 1985 1995
US Unemployment Rate
Process Point
• When you see the behavior, you should know which type of loop is a dominant loop
• E.g. if you observe exponential growth, you know there is at least one positive feedback (and possibly more)
• However, there will be many negative loops as well. But the positive loops are dominant
S-shaped growth
Time
Carrying Capacity
State of theSystem
BResourceAdequacy
CarryingCapacity
FractionalNet Increase
Rate
R
NetIncrease
Rate
+
+
+
-
+
+
State of theSystem
S-shaped growth condition
• S-shaped growth happens only 1. The negative loops must not include any
significant time delays2. The carry capacity must be fixed
• Carry capacity is the capability of an environment to handle that variable
• What are the examples of S-shaped behavior?
Example of S-shaped growth
0
100
200
300
0 14 28 42 56 70 84
Growth of Sunflowers
Days
0
25
50
75
100
1950 1960 1970 1980 1990 2000
US Cable Television Subscribers
% of Households with TVSubscribing to Cable
Cable Subscribers(Million Households)
0
25
50
75
100
1960 1962 1964 1966 1968 1970 1972
Adoption of Cardiac Pacemaker by Physicians
S-shaped growth with overshoot
• S-shaped structure with significant time delays in the negative loops
• Time delays in the negative loops lead to the possibility that the state of the system will overshoot and oscillate around the carrying capacity
• What are the examples of S-shaped growth with overshoot?
S-shaped growth with overshoot structure
Time
Carrying Capacity
State of theSystem
BResourceAdequacy
R
+
+
+
-
+
Delay
State of theSystem
FractionalNet Increase
Rate
NetIncrease
Rate+
Delay
CarryingCapacity
Example of S-shaped growth with overshoot
0
2
4
6
8
10
1800 1850 1900 1950 2000
Population of London
0
2500
5000
1900 1920 1940 1960 1980 2000
US Aluminum Production
Overshoot and Collapse
• Carrying capacity is reduced by the variables• E.g. the ability of the environment to support a
growing population is eroded or consumed by the population itself
• If there is no regeneration of the carrying capacity, the equilibrium of the system is extinction
• What are the examples of overshoot and collapse?
Overshoot and collapse structure
Time
Carrying Capacity
State of theSystem
B
R
NetIncrease
Rate
State of theSystem
+
+
+
-
+
+
B
Consumption/Erosion of
Carrying Capacity
-
+
ResourceAdequacy
CarryingCapacity
FractionalNet Increase
Rate
Example of overshoot and collapse
0
50
100
150
1880 1900 1920 1940 1960 1980 2000
New England Haddock Catch
0
10
20
30
40
1975 1977 1979 1981 1983 1985
Silver Prices
0
10
20
30
40
1950 1960 1970 1980 1990 2000
Net Change in World Nuclear Power Capacity
0.0
0.5
1.0
1.5
2.0
1976 1978 1980 1982 1984 1986
Sales of the Atari Corporation
What are the structures for these exponential growth behaviors?
0
2
4
6
1900 2000
0
2
4
6
0 400 800 1200 1600 2000
Bill
ion
Pe
op
le
Lower Bound
Upper Bound
Average Growth Rate:1900 - 1950: 0.86%/year (doubling time 80 years)1950 - 1997: 1.76%/year (doubling time 40 years)
0
300
600
900
1200
1920 1940 1960 1980 2000
Th
ou
sa
nd
Pe
op
le
Average Growth Rate:1926 - 1995: 3.5%/year (doubling time 20 years)1970 - 1995: 6.8%/year (doubling time 10 years)
0
3
6
1965 1970 1975 1980 1985 1990 1995 2000
80868080 80286386
486
Pentium
PentiumPro
Average Growth Rate:33%/year (doubling time: 2 years)
4004Best Fit Exponential
102
103
104
105
106
107
1965 1975 1985 1995
Mill
ion
Tra
ns
isto
rs/C
hip
0
4000
8000
1850 1900 1950 2000
Bill
ion
19
92
$/Y
ea
r Average Growth Rate 3.45%/yearDoubling Time 20 years
US Real GDP
World Population
US Prison Population
Transistors per Chip, Intel Microprocessors
Basic positive feedbacks responsible for economic growth
Expanding the model to include investment and births
Simple model of the demographic transition
First-cut model to explain growth in prison population
Prison population model expanded to include hypothesized social feedback
Prison population model expanded to include rewards and risk of crime
Selected positive feedbacks underlying Moore’s Law
What are the structures underlying these goal-seeking behaviors?
0
500
1000
1500
1987 1988 1989 1990 1991
Semiconductor Fabrication Defect Rate
Start of TQM Program
0
20
40
60
80
100
1978 1980 1982 1984 1986 1988 1990 1992
Nuclear Plant Load Factor
0
5
10
15
20
25
1950 1958 1967 1975 1983 1992
Television Share of All Advertising, US
0
5
10
15
20
25
1920 1940 1960 1980 2000
US Traffic Fatalities per Vehicle Mile
Process improvement efforts – PDCA
Process improvement for nuclear plant load
Feedbacks acting to improve automobile safety
Demand and supply for TV ads
TV ads model expands to include the audience annoyance loop
TV ads model expands to include couch potato and program quality
What are the structures underlying these oscillation behaviors?
-0.4
0.0
0.4
1850 1900 1950 2000
US Real GDP Deviation From Trend
70
75
80
85
90
95
1945 1955 1965 1975 1985 1995
Capacity Utilization, US Manufacturing
0
2
4
6
8
10
12
1945 1955 1965 1975 1985 1995
US Unemployment Rate
Negative feedbacks and delays contributing to the business cycle
Next Week
• Chapter 6• Research Proposal• 1 paragraph summarize of Navid’s paper
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